Apologies for the verbosity up-front, but I've given this problem quite a bit of thought. Coming at this from a pretty different angle:
1. Argument
P1: (Sol & Env Prob & ~Gov't Mandated) --> Changes to Cons Habits
P2: Change to Cons Habits --> Econ Enticing
--
C: ~Econ Enticing --> (Env Problem -m-> ~ Sol)
2. Cascading sufficient condition of conclusion through premises:
I viewed this problem as: if I am in the world where '~Econ Enticing' is held true (i.e. as is found in the conclusion, as the sufficient condition), how does that cascade through the premises? Specifically, taking the contrapositives in P2 and P1 and linking these statements takes me to:
~ Econ Enticing --> ~ Change to Cons Habits --> ~ (Sol & Env Prob & ~Gov't Mandated)
3. Setting up the goal:
My goal is thus to find a way to get from:
~ (Sol & Env Prob & ~Gov't Mandated) -- i.e. the resulting premises in the argument via the contrapositive chain from above.
to:
(Env Problem -m-> ~Sol) -- i.e. the necessary condition for the conclusion.
I re-phrased the 1st statement, by cascading the '~' through the & statements, as:
(~ Sol OR ~ Env Prob OR Gov't Mandated) -- (or colloquially: it must be the case that a) there is no solution, b) it is not to an environmental problem, or c) it is government mandated. ONE of these statements (or more) MUST necessarily be true.
4. Cascading sufficient condition of (Env problem -m-> ~sol) through premises:
First off, a point of clarity to clear any ambiguities. The conclusion is essentially a 'nested if' statement: ~Econ Enticing --> (Env Problem -m-> ~ Sol), where:
~Econ Enticing is the core sufficient condition (CSC)
Env Problem is the sufficient condition to the core necessary condition (SC-CNC)
~ Sol is the necessary condition to the core necessary condition (NC-CNC)
The way I thought about this was, if I assume that I am dealing with 'most environmental problems' (SC-CNC) what must absolutely take me to to the NC-CNC of '~Sol' from the premises? Remember, in the premises, I have (3) statements, (at least) one of which must be true, based off the cascading performed in step #2:
~ Sol
~ Env Prob
Gov't Mandated
I infer from 'Most environmental problems', that ~Env Prob is going to be FALSE, as a world where I am dealing with 'Most environmental problems' means that I necessarily have a single environmental problem; therefore, "~Env Prob" is a FALSE statement. I strike this one from the three options.
That means, if I assume '~Gov't Mandated', I am NECESSARILY left with ~Sol as the TRUE statement of my premises.
Thus, in a world where I assume 'Most environmental problems': to arrive at my SC-CNC + NC-CNC 'sub-conclusion' of (Env Problem -m-> ~ Sol), I can assume the NC-CNC is ~Gov't Mandated to arrive at '~Sol', which is PRECISELY what we see in Option (A).
Option (A) is diagrammed as:
Env (i.e. ecol) problem -m-> ~ Gov't Mandated
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Key takeaways for me:
- If a conclusion is phrased as a conditional statement, may be valid to assume the sufficient condition as 'TRUE', and determine how you can link the resulting inferences from the premises with the necessary condition of the conclusion
- For nested IF statements, as is seen in the conclusion here, the same takeaway as above can be applied
Very, very tricky problem; but hopefully this is helpful as a point of clarity for all.